Question

The sum of first n terms of three AP are S1 ,S2, S3 respectively. The first term of each AP is 1 and common difference are 1, 2, 3 respectively. Prove that S1 + S3 = 2S2.


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Answer 1

Step-by-step explanation:

Sum of n terms of three A.P. are S

1

,S

2

,S

3

respectively. If first term of each progression is 1 and common differences are 1,2,3 respectively, then prove that:

S

1

+S

3

=2S

2

Answer 2

Answer:

Solution:

» S1 = n/2 [2 + (n - 1)] ... (1)

» S2 = n/2 [2 + 2(n - 1)] ... (2)

» S3 = n/2 [2 + 3(n - 1)] ... (3)

Now, S1 + S3 = n/2 [4 + 4(n - 1)]

= 2n/2 [2 + 2(n - 2)]

= 2S2

Therefore, S1 + S3 = 2S2